Next let us imagine the sun contracted to a tenth of its present diameter, so that its atoms and electrons move ten times nearer to one another. Its mean density is thereby increased from 1·4 to 1400 times that of water, and its central density from about 140 to 140,000. You may check me here by pointing out that if the sun is already in a liquid state it cannot be compressed to any such extent—a liquid cannot usually have its density increased a thousand-fold. But we have already noticed that halving a star’s diameter doubles its temperature throughout. In the same way reducing a star’s diameter to a tenth increases its temperature ten-fold, so that the sun’s central temperature will be increased from, say, 50 million degrees to 500 million degrees. And at this latter temperature atoms hardly exist any longer as such—the stellar matter consists almost entirely of free electrons and nuclei. And these are so minute, that the increase of the sun’s mean density from 1·4 to 1400 times the density of water is not only possible, but leaves the sun’s substance in a state which may best be described as gaseous. Once again, then, the new sun is dynamically unstable. It would be represented by a point well to the left of the main-sequence, near the middle of the unoccupied region between the main-sequence and the white dwarfs, but as it is unstable it cannot maintain its position here. Again we see that even if we place a star in this region it cannot stay there. And, again—may it not be that the reason why this region is unoccupied is that it represents unstable stars? Once more you may check me. If I have made my point, it has been by the help of the rise of temperature which accompanies contraction. When we imagined the sun to expand, ought we not to have considered the fall of temperature which accompanies expansion? The answer is that we ought, but it would have made no difference. Lowering the temperature will cause a number of _L_-rings, and possibly also of _M_-rings, of electrons to re-form, so that the new atoms will be of larger size, but they will not lose their freedom of motion sufficiently to make the sun stable. It would have been different if we had been discussing a star of 10 or 50 times the sun’s weight; then it can be shewn that the re-formation of _K_- and _L_-rings would have produced a series of stable configurations. And the spur branch in the Russell diagram exists to provide a home for just such stars. The whole problem is too complicated to be discussed satisfactorily in this fragmentary way; its proper discussion involves very complicated mathematical analysis. Mathematical discussion shews that the Russell diagram can be divided into regions representing stable and unstable configurations in the manner shewn in fig. 24. [Illustration: Fig. 24. Stable and unstable configurations in the Russell diagram.]